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Size Matters, So Does Duration: The Interplay Between Offer Size and Offer Deadline

Author

Listed:
  • Zhenyu Hu

    (Institute of Operations Research and Analytics, National University of Singapore, Singapore 119260; Department of Analytics and Operations, Business School, National University of Singapore, Singapore 119245)

  • Wenjie Tang

    (Institute of Operations Research and Analytics, National University of Singapore, Singapore 119260; Faculty of Business, Economics, and Statistics, University of Vienna, 1090 Vienna, Austria)

Abstract

This paper investigates the interplay between offer size and offer deadline in a Stackelberg game involving a proposer and a responder. The proposer acts first by making an offer to the responder with a deadline, and the responder, concurrently following a continuous-time finite-horizon search for alternative offers, has to respond to the proposer’s offer by the deadline. Taking into account the responder’s reaction, the proposer’s optimal strategy can vary from an exploding offer—an offer that has to be accepted or rejected on the spot—to an offer with an extended deadline under different market conditions, proxied by characteristics of the alternative offer distribution. In particular, the proposer should offer an exploding offer when the alternative offer market is unfavorable to the responder, and the harsher it is, the smaller will be the offer size. By contrast, when the alternative offer market is favorable to the responder, the proposer can benefit from making a smaller (compared with the exploding offer) nonexploding offer, and the more favorable the market, the smaller will be the offer size and the longer the deadline. Our analysis is further extended to the case where the responder has private knowledge of the alternative offers’ arrival rate, and we characterize the optimal strategy for the proposer when she makes either a single offer or a menu of offers that serves as a self-selection mechanism. In the latter case, the optimal menu of offers can be implemented as a sign-up bonus type of contract.

Suggested Citation

  • Zhenyu Hu & Wenjie Tang, 2021. "Size Matters, So Does Duration: The Interplay Between Offer Size and Offer Deadline," Management Science, INFORMS, vol. 67(8), pages 4935-4960, August.
    • Handle: RePEc:inm:ormnsc:v:67:y:2021:i:8:p:4935-4960
    DOI: 10.1287/mnsc.2020.3731
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    References listed on IDEAS

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